Question

The figure below is a segment of a circle centre O radius r units.CM is the perpendicular bisector of AB. 

Given that CM=1cm and AB=2√3cm,

1. calculate the radius of the circle centre O from which the segment was cut 
2. calculate the angle that chord AB subtends at the centre of the circle 
3. hence calculate
   1. the length of arc ACB 
   2. the area of the segment AMBC

Answer 1

1. 
   
   r²=(r − 1)² + (√3)²    
   r² =r² − 2r + 1 + 3     
   2r = 4
   r=2cm    
2. Cos θ = ½ = 0.5
         θ =60º                   
   Angle at centre =120°   
3.  
   1.  ¹²⁰/₃₆₀ × 2 × ²²/₇ ×2 =4.190       
   2. ¹²⁰/₃₆₀ × ²²/₇ × 2² − ½ ×2² sin 120   
      =4.190 − 1.7321 = 2.4579